$\theta$-modular bands of groups
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Abstract:
The class of $\theta$-modular bands of groups is defined by means of a type of modularity condition on the lattice of congruences on a band of groups. The main result characterizes $\theta$-modularity as a condition on the multiplication in the band of groups. This result is then applied to the classes of normal bands of groups and orthodox bands of groups.References
- L. W. Anderson, R. P. Hunter, and R. J. Koch, Some results on stability in semigroups, Trans. Amer. Math. Soc. 117 (1965), 521–529. MR 171869, DOI 10.1090/S0002-9947-1965-0171869-7
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791
- C. Eberhart, W. Williams, and L. Kinch, Idempotent-generated regular semigroups, J. Austral. Math. Soc. 15 (1973), 27–34. MR 0320185, DOI 10.1017/S1446788700012726
- T. E. Hall, On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. 1 (1969), 195–208. MR 249527, DOI 10.1017/S0004972700041447
- Gérard Lallement, Congruences et équivalences de Green sur un demi-groupe régulier, C. R. Acad. Sci. Paris Sér. A-B 262 (1966), A613–A616 (French). MR 207872 M. Petrich, Topics in semigroups, Pennsylvania State University, University Park, Pa., 1967. —, Regular semigroups satisfying certain conditions on idempotents and ideals (to appear).
- N. R. Reilly and H. E. Scheiblich, Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349–360. MR 219646, DOI 10.2140/pjm.1967.23.349
- H. E. Scheiblich, Certain congruence and quotient lattices related to completely $0$-simple and primitive regular semigroups, Glasgow Math. J. 10 (1969), 21–24. MR 244425, DOI 10.1017/S0017089500000483
- C. Spitznagel, The lattice of congruences on a band of groups, Glasgow Math. J. 14 (1973), 187–197. MR 330332, DOI 10.1017/S0017089500001956
- C. Spitznagel, The lattice of congruences on a band of groups, Glasgow Math. J. 14 (1973), 187–197. MR 330332, DOI 10.1017/S0017089500001956
- Miyuki Yamada and Naoki Kimura, Note on idempotent semigroups. II, Proc. Japan Acad. 34 (1958), 110–112. MR 98141
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 177 (1973), 469-482
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0318365-6
- MathSciNet review: 0318365